`intxtan^2xdx`
Rewrite the integrand using the identity `tan^2x=sec^2x-1`
`intxtan^2xdx=intx(sec^2x-1)dx`
`=intxsec^2xdx-intxdx`
Now let's evaluate `intxsec^2xdx` using integration by parts,
`intxsec^2xdx=x*intsec^2xdx-int(d/dx(x)intsec^2(x))dx`
`=xtan(x)-int(1*tan(x))dx`
`=xtan(x)-int(sin(x)/cos(x))dx`
Substitute cos(x)=t
-sin(x)dx=dt
`int(sin(x)/cos(x))dx=int-dt/t`
`=-ln|t|`
substitute back t=cos(x),
`=-ln|cos(x)|`
`intxsec^2xdx=xtan(x)-(-ln|cos(x)|)`
`=xtan(x)+ln|cos(x)|`
`intxtan^2(x)dx=xtan(x)+ln|cos(x)|-intxdx`
`=xtan(x)+ln|cos(x)|-x^2/2+C`
C is a constant
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